On the Maximum Degree of a Random Planar Graph

DOI10.1017/S0963548308009097zbMath1160.05018OpenAlexW2042502099MaRDI QIDQ3527545

Colin J. H. McDiarmid, Bruce A. Reed

Publication date: 29 September 2008

Published in: Combinatorics, Probability and Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0963548308009097

zbMATH Keywords

Maximum degreeEmbeddable graphMaximum face sizeRandom planar graph

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35) Random graphs (graph-theoretic aspects) (05C80) Planar graphs; geometric and topological aspects of graph theory (05C10)

Related Items (18)

Maximum degree in minor-closed classes of graphs ⋮ Classes of graphs embeddable in order-dependent surfaces ⋮ The maximum degree of random planar graphs ⋮ Concentration of maximum degree in random planar graphs ⋮ Random graphs from a weighted minor-closed class ⋮ Longest and shortest cycles in random planar graphs ⋮ The evolution of random graphs on surfaces ⋮ Modularity of minor‐free graphs ⋮ The Evolution of Random Graphs on Surfaces ⋮ Phase transitions in graphs on orientable surfaces ⋮ Random graphs on surfaces ⋮ Random Graphs from a Minor-Closed Class ⋮ The Maximum Degree of Series-Parallel Graphs ⋮ Spanning embeddings of arrangeable graphs with sublinear bandwidth ⋮ Random graphs from a block-stable class ⋮ The maximal degree in a Poisson-Delaunay graph ⋮ Two critical periods in the evolution of random planar graphs ⋮ Unnamed Item

Cites Work

• On-line routing of random calls in networks
• Random planar graphs
• The distribution of the maximum vertex degree in random planar maps
• Congruent Graphs and the Connectivity of Graphs

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